MA19.8.9
Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.
Interpret y = mx + b as defining a linear equation whose graph is a line with m as the slope and b as the y-intercept.
UP:MA19.8.9
Vocabulary
- Slope
- Rate of change
- Initial Value
- Y-intercept
Knowledge
Students know:
- how to graph points on a coordinate plane.
- Where to graph the initial value/y-intercept.
- Understand how/why triangles are similar.
- how to interpret y=mx equations.
Skills
Students are able to:
- create a graph of linear equations in the form y = mx + b and recognize m as the slope and b as the y-intercept.
- point out similar triangles formed between pairs of points and know that they have the same slope between any pairs of those points.
- Show that lines may share the same slope but can have different y-intercepts.
- Interpret a rate of change as the slope and the initial value as the y-intercept.
Understanding
Students understand that:
- Slope is a graphic representation of the rate of change in linear relationships and the y-intercept is a graphic representation of an initial value in a linear relationship.
- When given an equation in the form y = mx + b it generally symbolizes that there will be lines with varying y-intercepts. even when the slope is the same.
- Use of the visual of right triangles created between points on a line to explain why the slope is a constant rate of change.
